Ernesto baked 3 cakes in 2 1/2 hours. assume that the number of cakes baked varies directly with the number of hours. write and solve a direct variation equation to find how many cakes can be baked in 7 1/2 hours.

Sam claims that cos x =sin y if x and y are congruent angels. is sam correct ?

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?